Preheat oven to 350°F. Prepare a muffin pan by lining with cupcake liners or lightly coating with baking spray.
In the bowl of a blender or food processor, add the carrots, sugar, coconut oil, aquafaba, chickpeas, coconut, and pecans, and pulse until just combined. In a separate bowl, combine the flour, baking soda, salt, cinnamon, nutmeg, and baking powder. Add the carrot mixture to the flour and mix until combined.
Divide the batter evenly into the muffin pan.
Bake in the oven for about 20 minutes, or until a toothpick inserted in the center comes out clean.
Let it rest in the muffin pan for 1 minute, then transfer to a wire rack to cool.
Make the non-dairy cream cheese frosting:
In a medium bowl, whisk together the cream cheese, butter, sugar, and vanilla. If the frosting is too thin to spread or pipe, chill in either the refrigerator or freezer (don't forget about it!) until it’s a workable consistency.
* If you have bagged pre-shredded carrots, this saves a step in the preparation!